This invention relates to electronic filters, and more particularly to digital filters having a controllable pass band.
In the field of information processing, it is widely recognized that information may be contained within any of a wide variety of formats, among which are electrical signals of either an analog or a digital nature. It is further recognized that there are applications in the field of information processing wherein it may be desirable to change the format in which information is contained. Typical of such applications are those wherein a somewhat specialized information processing operation may be necessary. In such applications, it is possible that the desired information processing operation may be more efficiently performed with information in one format than another. By way of illustraton, if information is contained within an analog format, and a desired operation thereon is most efficiently performed by employing digital techniques, it would be necessary to translate the information from the analog format to the digital format for the performance of the desired processing operation. Thereafter, the information could be again translated back to the original analog format. Consequently the process of translation of format of information, particularly between analog and digital formats, has received considerable attention.
There are a number of considerations attendant to the translation between analog and digital formats. One such consideration relates to the number of digital samples of an analog signal which are necessary to faithfully reconstruct an original analog signal from the collection of digital samples thereof. In this regard, it has long been recognized that, according to the widely recognized Nyquist Criteria, a sampling rate of greater than twice the highest frequency of interest in the original analog signal will suffice to reconstruct the original analog signal from the collection of digital samples thereof. However, in addition to the foregoing consideration with respect to a minimum sampling rate, it has been observed that further considerations are involved with respect to the frequency spectrum content of the original analog signal. In particular, it has been observed that while the sampling of an analog signal at a rate of greater than twice the highest frequency of interest therein will result in a sufficient number of samples to reconstruct the original signal therefrom, the presence of frequencies in the original analog signal above one-half of the sampling frequency results in undesirable effects in the subsequent reconstruction process of the original analog signal. In particular, the presence of such frequencies results in the subsequent generation of additional unwanted signals in the signal subsequently reconstructed from the digital samples. This phenomenon is referred to as "aliasing distortion", and requires for its avoidance that frequencies above one-half of the sampling frequency must be removed from the analog signal prior to the sampling thereof. The desired removal process is typically performed by a low pass filtering process having a cut off frequency greater than the highest frequency of interest in the original analog signal and less than one-half the sampling rate. This removal process, broadly referred to as anti-aliasing filtering, must be performed upon the analog signal prior to the sampling process.
In some applications involving anti-aliasing operations, the cut off frequency of the anti-aliasing filtering operation remains fixed. However, there are other applications which require an adjustable cut off frequency. An illustration of a typical application involving the generation of a video image of a reduced size will serve to illustrate the salient considerations involved. It should be understood, however, that while the following discussion with respect to a video image will illustrate the consideration associated therewith, there are likewise similar considerations associated with other applications which would be apparent to one of ordinary skill in the art. Consequently the following discussion with respect to video signal processing is not to be interpreted in a limiting manner.
It is frequently desirable in dealing with video images to reduce the size of a first video image by a selected amount, and to thereafter insert the resulting reduced size video image into a second video image. Typical of such operations are the familiar inserting of a first video image in a selected area of a second video image, frequently seen in television sports or news broadcasts. While the foregoing process may be performed in a variety of ways, one way typical of the process employing digital signal processing would involve the following steps. Assuming a desired video image to be inserted into the second video image is originally in an analog signal format, the video information contained therein would first be filtered employing analog filtering techniques to remove frequency components above a selected frequency of interest. Thereafter, the analog signal waveform would be sampled at a rate determined by the highest frequency of interest therein, and the digital samples so obtained stored in a suitable manner. This first anti-aliasing filtering operation is of course required to ensure that in a subsequently reconstructed video image identical to the original, frequencies present above the selected frequency are removed and cannot generate unwanted signals in the subsequently reconstructed video image. However, a second anti-aliasing filtering process is required in connection with the production of a video image of reduced size. This second anti-aliasing filtering process follows from the requirement that frequencies associated with the anti-aliasing phenomenon must be removed prior to the sampling process associated therewith. In particular, the production of a video image of reduced size involves selection of digital values from among the collection of digital samples previously collected. This selection process is equivalent to a re-sampling process. Consequently, prior to the selection of digital values for the construction of the reduced size video image, from among the set of ditigal samples previously collected, it is necessary to again perform an anti-aliasing filtering operation upon the set of digital samples previously collected. The cut off frequency associated with the anti-aliasing filter in this second anti-aliasing filtering process is determined by the desired size of the reduced video image. Consequently it is observed that in the process of producing video images of selected reduced size requires an anti-aliasing filter having an adjustable cut off frequency.
While the foregoing has described the necessity of the filtering process in connection with the production of a video image of a reduced or compressed size, it will be recognized by one skilled in the art that similar filtering operations are likewise necessary in connection with fixed rotations of video images. Broadly stated, it is recognized that in dealing with either compressions or rotations of video images of a fixed amount, an anti-aliasing filtering process in necessary. In particular, the cut off frequency associated with the anti-aliasing filtering apparatus is determined by the desired amount of rotation or compression of the video iamge. It should be noted in this respect that for a selected amount of compression or rotation of a video image, the corresponding cut off frequency of the anti-aliasing filter is a constant. In particular, it is only necessary to change the cut off frequency of the anti-aliasing filtering apparatus when the amount of compression or rotation of the video image is changed. Consequently, it is recognized that for a selected amount of compression or rotation of a video image, the cut off frequency of the associated anti-aliasing filtering apparatus is a constant frequency determined by the parameters associated with the amount of compression or rotation of the associated video image.
However, while video image processing involving the compression or rotation of a video image by a fixed amount requires a corresponding static alteration of the cut off frequency of the associated anti-ailasing filtering apparatus, it will likewise be recognized by one skilled in the art that there are applications in video image processing wherein the cut off frequency associated with the anti-aliasing filtering operation is not a constant, but requires alteration in a dynamic manner. Broadly stated, applications which involve three dimensional perspective operations require that the cut off frequency of the anti-aliasing filtering apparatus be altered in a dynamic manner. In particular, in applications wherein it is desirable to process a selected video image in such a manner to produce the effect of a perspective projection. e.g., it is desired that the selected video image appear as projected into a three dimensional space in such a manner as to appear rotated either inward to or outward from the three dimensional space, the necessary resulting video image will require compression and rotation in varying amounts determined by the amount of desired projection with respect to the three dimensional space. In the video image processing associated with the production of such an image, the cut off frequency of the anti-aliasing filter must be dynamically adjusted in accordance with the changing amounts of compression and rotation necessary to achieve the three dimensional effect. Consequently, the processing of video images in such a manner to achieve three dimensional perspective effects requires dynamic alteration of the cut off frequency of the associated anti-aliasing filtering apparatus.
It will likewise be recognized by one skilled in the art that as the selected video image is comprised of a set of discrete samples which occur at a constant rate in a video scan line order, the aforedescribed anti-aliasing filtering operation must likewise occur at the same constant rate. It should be particularly noted in this regard with respect to video image processing involving three dimensional perspective effects, that the cutoff frequency of the anti-aliasing filter must correspondingly vary as the sequence of samples flows into the anti-aliasing filter. Consequently, as the discrete samples are necessarily supplied at a relatively high rate, the associated cut off frequency of the anti-aliasing filter must correspondingly be capable of varying at the same relatively high rate. This has been accomplished in the past in a number of ways. Once such approach has employed the use of Infinite Impulse Response digital filters, hereinafter referred to as IIR filters. Broadly speaking, an IIR filter typically involves the use of a storage element in a main signal path through the IIR filter, with associated feedback paths to achieve the desired filtering. Digital multipliers are typically employed in the design of IIR filters. In such a design, the response of an IIR filter may be dynamically altered by changing a multiplicand associated with one or more of the digital multipliers. However, while an IIR filter does provide a filtering operation with a degree of dynamic control over the cut off frequency associated therewith, IIR filters further have associated therewith a number of disadvantages, including a phenomenon relating to the storage of previous responses. Such disadvantages tend to make the use of IIR filters less than desirable in implementing anti-aliasing filter operations where a high degree of dynamic control over the cut off frequency is necessary.
In an alternate approach, a Finite Impulse Response digital filter is frequently employed. A Finite Impulse Response digital filter, hereinafter referred to as a FIR filter, is generally comprised of a plurality of digital delay devices, a digital adder, and a plurality of digital multiplier devices. In such a filter, the cut off frequency may be altered by adjustment of the values of the multiplicands associated with the multiplier devices. It has been found that the FIR filter does indeed provide the required high degree of dynamic control required over the cut off frequency associated with an anti-aliasing filter operation. However, there is likewise a significant practical disadvantage associated with the use of FIR filter designs. In particular, prior art FIR filter designs require the use of a plurality of multipler devices; frequently one multiplier device per digital delay device employed in the FIR filter. The disadvantage which follows from the use of an FIR filter design to implement a anti-aliasing filter operation results from the economic cost associated with the digital multiplier devices required therein. In particular, digital multiplier devices are comparatively expensive. Consequently, while anti-aliasing filters implemented as FIR filters do offer higher desirable performance characteristics, the price of the digital multiplier devices required therein has been a significant unavoidable disadvantage. There is consequently a need for a filter having a dynamically controllable variable cut off frequency which requires fewer digital multiplier devices than the FIR approach.